Beam Bending and Moments of Inertia

[ACE_99]

Homework Statement

This is a two part question. In the first part you are asked to determine the mam moment that can be applied to the beam if it is bent about the z axis. They then ask you to redo the question bending about the y axis. This is probably a really simple question but what is the difference in bending about different axis? I understand what I need to do in order to solve the question I'm just having trouble visually picturing and understanding what the difference is when you bend it about the y-axis and when you bend it about the z axis. I've posted the solutions that were provided to me by my prof. In this question I'm unsure why it is they use the parallel axis theorem to calculate the moments of inertia of pieces 1 and 3.

Sorry if this is posted in the wrong place.

 

[mathmate]

First, since it usually takes a certain time before attachments are approved for display to the public, we are not yet able to see your illustration. Your description alone permits me to make a guess, but not understand your problem.

It sounds to me that it is a problem of a beam section where the second moment of area is different between the y and z axes. You may be required to calculate the properties and given the maximum stress, calculate the maximum moment allowable at this section.

You are likely to get faster responses if you post your attachments (.jpg) at a photo server and post us the link. Sometimes it takes a couple of days to get the attachment approved.

 

[ACE_99]

Actually mathmate that's exactly what the problem is asking. In the question just before this one they asked us to calculate it about the z axis. Heres a link to the image.

 

[mathmate]

The example does the more difficult part, where the y-axis does not pass through the centroid of each of the component rectangles, thus the calculation of second moment of area (loosely called moment of inertia by most civil engineers) for the section requires the use of the parallel axis theorem.

In the case of the z-axis, the axis passes through the centroid of the three rectangles, therefore the second moment of area is simply the sum of the three components calculated through the centroid using the formula
Izz=bd³/12
After that, the simple application of the formula
\sigma = My/I
should be no mystery to you.

 

[ACE_99]

Great thanks a lot for the help.